Browser is getting worse and worse, videos don't play half the time.
HD videos and gifs don't play most the time. And videos in facebook don't work.
Opaite Mbohovái (1)
Firefox sees two different versions of Flash as being installed.
Shockwave Flash 24.0 r0 Shockwave Flash 23.0 r0
Grab the Adobe uninstaller from here and use it to completely remove Flash: http://helpx.adobe.com/flash-player/kb/uninstall-flash-player-windows.html
Then install the latest version of Flash for Firefox.
See if that solves some or all of your issues with playing videos.